TY - JOUR
T1 - Numerical computations for long-wave short-wave interaction equations in semi-classical limit
AU - Chang, Qianshun
AU - Wong, Yau Shu
AU - Lin, Chi Kun
N1 - Funding Information:
We would like to thank Professor Tang Tao, Professor W.-Z. Bao and the referees for their valuable comments and suggestions leading to the improvement of the manuscript. Q.S. Chang and C.K. Lin would like to thank the Department of Mathematics & Statistical Science, University of Alberta for the hospitality during their stay. This research was supported in part by the Natural Sciences and Engineering Research Council of Canada. The research of CKL was also supported in part by National Science Council of Taiwan under the Grant 95-2115-M-009-MY3 and 5-500 of College of Science, NCTU.
PY - 2008/10/1
Y1 - 2008/10/1
N2 - This paper presents and compares various numerical techniques for the long-wave short-wave interaction equations. In addition to the standard explicit, implicit schemes and the spectral methods, a novel scheme SRK which is based on a time-splitting approach combined with the Runge-Kutta method is presented. We demonstrate that not only the SRK scheme is efficient compared to the split step spectral methods, but it can apply directly to problems with general boundary conditions. The conservation properties of the numerical schemes are discussed. Numerical simulations are reported for case studies with different types of initial data. The present study enhances our understanding of the behavior of nonlinear dispersive waves in the semi-classical limit.
AB - This paper presents and compares various numerical techniques for the long-wave short-wave interaction equations. In addition to the standard explicit, implicit schemes and the spectral methods, a novel scheme SRK which is based on a time-splitting approach combined with the Runge-Kutta method is presented. We demonstrate that not only the SRK scheme is efficient compared to the split step spectral methods, but it can apply directly to problems with general boundary conditions. The conservation properties of the numerical schemes are discussed. Numerical simulations are reported for case studies with different types of initial data. The present study enhances our understanding of the behavior of nonlinear dispersive waves in the semi-classical limit.
KW - Finite-difference schemes
KW - Long-wave short-wave interaction equations
KW - Numerical methods
KW - Semi-classical limit
UR - http://www.scopus.com/inward/record.url?scp=49349105565&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2008.05.015
DO - 10.1016/j.jcp.2008.05.015
M3 - Article
AN - SCOPUS:49349105565
SN - 0021-9991
VL - 227
SP - 8489
EP - 8507
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 19
ER -